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icang [17]
3 years ago
11

Solve the system of equations 2x+2y=6z=8 5x+6y+5z=3 5x+6y+3z=5

Mathematics
1 answer:
Alborosie3 years ago
4 0

Answer:

x=34,y=-27andz=-1

Step-by-step explanation:

Given:

2x+2y+6z=8  equation:1

5x+6y+5z=3     equation:2

5x+6y+3z=5     equation:3

We have to find the value of x,y and z

Eliminating two variables to find the value of third variable

Subtracting  equation:2 from equation:3

         

5x+6y+3z-(5x+6y+5z)=5-3

5x+6y+3z-5x-6y-5z=2\\-2z=2\\z=-1

Solving the equation:1 for 'x'

2x+2y+6z=8

2x=8-2y-6z\\2x=8-2y-6(-1)\\2x=8-2y+6\\2x=14-2y\\x=7-y

Putting x and z in equation 2

5(7-y)+6y+5(-1)=3\\35-5y+6y-5=3\\y+30=3\\y=3-30\\y=-27

Putting the value of 'y' and 'z' in equation:2 to find the value of 'x'

5x+6(-27)+5(-1)=3\\5x-162-5=3\\5x-167=3\\5x=3+167\\5x=170\\x=\frac{170}{5}\\ x=34

The values of x,y and z are

x=34,y=-27andz=-1

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